Estudo de alguns metodos determinsticos de otimização irrestrita

• Ano de defesa: 2010
• Autor(a) principal: Brandão, Milena Almeida Leite
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: Otimização matemática; Análise numérica; Otimização irrestrita; Otimização determinstica; Metodos classicos de otimização; Metodos de busca linear; Unconstrained optimization; Deterministic optimization; Classical methods of optimization; Line search methods; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16782

In this work some classical methods of linear search for unconstrained optimization are studied. The main mathematical formulations for the optimization problem are presented. Two strategies, linear search and trust region, for the algorithm to move from one iteration to another are discussed. Furthermore, the main considerations about the choice of step length along the search direction to ensure the convergence of the methods are exposed. Among the methods studied, some methods minimize a function of several variables without using derivatives (Cyclic Coordinates, Hooke and Jeeves with line searches and discrete steps and Rosenbrock). In the other methods the search direction is obtained by using derivatives of the objective function (Steepest Descent, Newton, Davidon-Fletcher-Powell, Broyden-Flotcher-Goldfarb-Shanno and Conjugate Gradient). For illustration, two optimization problems, one theoretical and one practical, are solved using the methods mentioned. The results are analyzed and comparisons between the studied methods are presented.